Solitons in a Hamiltonian $PT$-symmetric coupler

TL;DR

This paper introduces a Hamiltonian $PT$-symmetric nonlinear coupler supporting stable bright solitons with nearly-integrable dynamics, despite gain and loss, and discusses its physical relevance to Bose-Einstein condensates.

Contribution

The work presents a novel Hamiltonian $PT$-symmetric dispersive coupler with conservation laws and exact soliton solutions, highlighting its stability and integrability features.

Findings

Bright solitons are numerically shown to be stable.

Solitons undergo elastic collisions, indicating near-integrability.

The model has potential applications in Bose-Einstein condensates.

Abstract

We introduce a nonlinear parity-time-symmetric dispersive coupler which admits Hamiltonian and Lagrangian formulations. We show that, in spite of the gain and dissipation, the model has several conservation laws. The system also supports a variety of exact solutions. We focus on exact bright solitons and demonstrate numerically that they are dynamically stable in a wide parameter range and undergo elastic interactions, thus manifesting nearly-integrable dynamics. Physical applications of the introduced model in the theory of Bose-Einstein condensates in nonlinear lattices are discussed.